Recent research at the interface of chemistry, condensed matter physics, and quantum optics has opened novel means to control chemical systems using quantum light. One manifestation of light-matter coupling occurs through controlling chemical systems within an optical cavity. The coupled light-matter system is describable by non-Hermitian physics, characterized by gain through laser pumping and loss through cavity dissipation. Non-Hermitian systems possess the capacity for exceptional point (EP) singularities where energy eigenvalues and eigenvectors become coalesce. To study the physics of EPs in strongly coupled light-matter systems I joined the Flatiron Institute as a guest researcher.

Building off of the Flatiron's existing density functional theory (DFT) numerical methods in Octopus, my role focused on extending the capabilities of numerical methods to account for imaginary eigenvalues present in non-Hermitian systems. To that end, I proved that the subclass of non-Hermitian systems, those characterized as pseudo-Hermitian, are amenable to DFT's underpinnings of the Hohenberg-Kohn theorem and the Kohn-Sham equations. Given the foothold of implementing EPs using pseudo-Hermitian Hamiltonians, I studied the topological properties produced by generating EPs in simple molecular systems.

Beyond the existence proof and simulations, working in tandem on the fundamentals of EP physics, particularly stacking exceptional points for designer phase accumulation along with exploring additional symmetries that lead to EP formation, and later testing theory through numerical simulation is a hopeful path in this line of research.

Fig. 1: Tailoring chemical and physical phenomena through light-matter coupling has far-reaching potential implications.^[1]

[1] Engineering quantum materials with chiral optical cavities